Counting loop diagrams: computational complexity of higher-order amplitude evaluation

• Published in: The European physical journal. C, Particles and fields Vol. 36; no. 4; pp. 459 - 470
• Main Authors: van Eijk, E., Kleiss, R., Lazopoulos, A.
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer Nature B.V 01.08.2004
• Subjects: Algorithms; Amplitudes; Asymptotic properties; Closed loops; Complexity; Feynman diagrams; Graphs; Symmetry

We discuss the computational complexity of the perturbative evaluation of scattering amplitudes, both by the Caravaglios-Moretti algorithm and by direct evaluation of the individual diagrams. For a self-interacting scalar theory, we determine the complexity as a function of the number of external le...